From the course: Learning Minitab

Comparing variances in Minitab - Minitab Tutorial

From the course: Learning Minitab

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Comparing variances in Minitab

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- [Instructor] In this movie, I will show you how to compare variances using Minitab. Open exercise file 05_02. Here we have four offices, A, B, C, D, with the processing times. Let's assume we want to see if the variance of office A is less than a target value of 9.0. So go to Stat, Basic Stats, 1 Variance Test. Our data are each in its own column, so let's select that. Select A. We want to perform a hypothesis test against a hypothesized variance of 9.0. Go to Options. 95% confidence level is fine. But the alternate hypothesis is less than the hypothesized variance of 9.0. OK and OK. Let's go full screen. Here we can see the methods used. The Bonett method is valid for any continuous distribution, whereas chi-square method is valid only for normal distributions. These are the stats with the intervals, the hypothesis, and the P-values. Notice both P-values are lower than 0.05, therefore we reject the null hypothesis and say that A's variance is indeed less than 9.0. Now, what if I want to compare two variances, let's say office A versus office D, to see which one has a higher variance or if they're equally consistent or inconsistent. So to compare variances, I would run a 2 variance test. Stat, Basic Stats, 2 Variances. Both samples are in separate columns. So A for the first sample, and D for the next one. Go to Options. Our ratio is a ratio of variances. Confidence level is fine. The hypothesized ratio of 1 makes sense because we're testing for differences between the two. The alternate would be not equal to, that's correct. OK and OK. Here we have the stats, the ratio of the variances. The Bonett method is more powerful. However, if you have fewer samples and skewed data, the Levene method is better. Regardless, notice that both intervals include 1.0. This is confirmed by the P-values. Both are relatively high compared to 0.05. Therefore, we fail to reject the null hypothesis. This is visually confirmed by the intervals here for the ratio. The overlap for the variances and the boxplots are here. And there you have it. That's how you compare two variances. Now what if I want to compare the variances of all four offices? Then I'll go to STAT, ANOVA, Test for Equal Variances. Our data in separate columns, so that's fine. And for the selection, let's choose all four. For Options, 95% confidence level is fine. OK. And for Graphs, let's choose Boxplots, and OK. And here we have the null and alternate hypothesis, and alpha 0.05 based on our confidence level. And here we have the confidence intervals for the standard deviations. And we have two methods involved here. The multiple comparisons test is for normal data. The Levene's test is valid for non-normal data as well. So regardless, at 0.000, both values are less than our alpha of 0.05, therefore reject the null hypothesis and conclude that at least one variance is different. This conclusion is confirmed usually by looking at these graphs. You can see that the intervals do not all overlap, and the boxplots are over here for illustrative purposes. So that's how you compare multiple variances. In summary, to compare one variance to a target, go to Stat, Basic Stats, 1 Variance Test, and for two variances, 2 Variance Tests. For multiple variances, go to Stat, ANOVA, Test for Equal Variances. So that's how you compare variances in Minitab.

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